US4926186A - FFT-based aperture monitor for scanning phased arrays - Google Patents

Abstract

Method and means for monitoring the performance of a phase array antenna. The antenna comprises an array of individual radiating element seach of which radiates a prescribed proportion of the energy to be transmitted thereby shaping such energy into a beam. Individual phase shifters are associated with each radiating element, the phases of which control the direction of the beam pointing. The method of the invention involves sampling the beam by means including a single receiver located along a fixed radial from the array. The beam scans at a constant rate. The samples are collected at non-uniform intervals of time during a beam scan. The samples are, however, separated by equal increments of arcsine θ, where θ is the pointing angle of the beam. The samples are analyzed by means including a Fourier transform to provide the value of the amplitude and phase of the signal radiated by each of the radiating elements. Comparison of the amplitude and phase values for each radiating element as determined by analysis with design values for each element reveals any element or phase shifter which may be faulty. The method can also be used to calibrate an antenna when it is first put into service.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to phased array antennas. More particularly it relates to a system and method for monitoring the signal radiated by a phased array antenna which provides an indication of faults in components of the antenna and identification of the faulty components. The invention also provides an accurate and convenient method for calibrating a phased array antenna for initial use.

Phased array antennas are found in a variety of applications primarily because of their ability to produce a radiation pattern of specified characteristics which may be steered electronically to any desired angle within certain coverage limits. The phased array antenna application of particular interest herein is in the Scanning Beam Microwave Landing System, but it is to be understood that the invention may be used in conjunction with phased array antennas in other applications.

2. Description of the Prior Art

A linear phased array antenna used in a Scanning Beam Microwave Landing System is described in U.S. Pat. No. 3,999,182 issued Dec. 21, 1976 to A. W. Moeller et al. In this antenna a plurality of radiating elements are spaced equally along a linear axis. The elements of the array lying to the left and to the right of the center element are each fed r.f. energy through individual electronically variable phase shifters, each of which is coupled into right and left branching series feed lines through individual directional couplers. The center elements of the array and the right and left branch series feed lines are coupled to a common microwave source through a four-way directional coupler.

The number of radiating elements and associated phase shifters and couplers present in an array is dependent upon such design factors as the desired beam width and sidelobe levels of the radiation pattern of the array and the scan angle coverage of the array. The elevation antenna described in the referenced patent includes eighty-one directional couplers and provides a radiation pattern of 1° beam width with a maximum sidelobe level of -27 dB. The scan angle coverage is from 0° to +20° in elevation.

Specific radiation pattern characteristics of the array require that each element coupler be designed to supply a precisely determined portion of power from the feed to the associated element and that each element be coupled into the feed with a particular insertion phase. The numerous components involved in a phased array antenna increase the number of sources of possible failure in the system. In compensation, however, a failure occurring in any one component does not result in total failure of the system but only results in a marginal degradation in beam quality. As the number of failed components increases, the beam quality decreases correspondingly until the deterioration exceeds a tolerable level and the system can no longer be safely used.

Monitoring systems have heretofore been used in conjunction with phased array antennas in the Microwave Landing Systems to warn of impending or actual system failure or to identify specific component failures, such as a diode failure in a digital phase shifter. One such monitor system comprises a receiver located at some distance from the antenna along a particular radial or elevation angle. The equivalent of a receiver located at a fixed point in the far field of the antenna is provided by an integral monitor usually comprising a slotted waveguide extending the length of the antenna array in close proximity thereto. Energy from the antenna array is coupled into the waveguide through the slots with the proper phases to produce a signal at the waveguide output corresponding to the signal which would be received at a distant point along a fixed radial from the array. The detected signal from the distant receiver or integral monitor provides data from which the beam main lobe and sidelobe signal strengths and pointing angles can be measured. Comparison of measured values of these quantities with stored values of similar quantities obtained during calibration of the array can reveal departure of the system performance below an acceptable level. Such a monitor is suitable for on-line executive use to alert operating personnel to the need to remove the system from service for maintenance. Such a monitor does not identify the system component or components at fault. Further measures must be taken to isolate and correct or compensate for the malfunction. These additional measures are taken while the array is out of service and involve determining the amplitude and phase of the monitor signal for each element of the array, element by element.

One disadvantage of such prior methods of fault identification and fault compensation of a phased array is the necessity to provide a highly efficient r.f. switch for each element of the array. Another disadvantage is that the test procedures cannot be conducted while the array is operating in service.

The present invention is in a method of processing data from a distant monitor receiver or from an integral monitor antenna which is capable of detecting and identifying non-time varying amplitude and phase faults as to each element of a phased array antenna during on-line operation of the array.

It is an object of the invention to provide a monitoring system for a phased array antenna capable of identifying special faults in the antenna during operation of the antenna in service.

It is another object of the invention to provide a monitoring system for a phased array antenna capable of determining phase insertion errors for each radiating element of the array.

Still another object of the invention is to provide a monitoring system for a phased array antenna capable of identifying particular elements of the array having faults in their associated r.f. feedlines, couplers or connectors.

It is a further object of the invention to provide a monitoring system for a phased array antenna capable of automatically calibrating the array to provide specific phase correction factors to compensate for phase shifter errors resulting from manufacturing tolerances.

Briefly, the invention comprises a method of sampling and processing data collected by a single monitor receiver located in the far field of a scanning phased array antenna, or by an equivalent integral monitor, which enables the antenna illumination function to be received. The beam transmitted by the antenna scans at constant rate between maximum scan angles of +θ₀, -θ₀, θ being the angle between the axis of the beam and the normal to the axis of the array. The output of the monitor receiver is sampled at non-uniform intervals of time. The sampling interval does, however, correspond to equal intervals of the arcsine of the scan angle θ.

The data collected by the monitor receiver is processed by a Fast Fourier Transform (FFT) to provide a recovered illumination function. The recovered illumination function shows the relative amplitude and phase of the energy distributed across the array aperture which created the received signal. Comparison of the recovered illumination function at each sampling point with design values of the illumination function for each element of the array reveals any specific array element at which the amplitude or phase has departed from allowable tolerance.

An amplitude fault usually requires removal of the array from service for repair of the r.f. transmission line, connectors or couplers associated with the faulty array element. Phase faults may be of such nature that correction can be accomplished by simply adding a compensating factor to the phase increment generated for the faulty element by the system beam steering unit. Since the invention identifies the particular element or elements of the array responsible for any degraded performance of the array, the down-time required for repair of the system is much less than in a system having a monitor which warns only of unacceptable performance.

The invention is based upon the accepted theory that the radiation pattern of an antenna can be synthesized from a known aperture illumination function by computing the Fourier transform of the illumination function.

A plurality of receivers placed with equal spacing along a line of length subtending an angle θ=arc sin(λ/d),

where d is the interelement spacing of the array, would provide n individual signals which may be vectorially summed to provide the Discrete Fourier Transform (DFT) of the illumination function. Then the Inverse Fourier Transform (IFT) of the DFT provides the reconstructed array illumination function.

By sampling the output of a single monitor receiver at non-uniform intervals the invention provides data equivalent that which would be provided by the above described plurality of receivers. Specifically, the time at which the monitor receiver output is sampled is determined by the relationship: ##EQU1## where t_k is the time interval between commencement of the antenna beam scan and the Kth sample;

λ is the wavelength of the radiated energy;

d is the spacing between radiating elements of the array;

N is the number of radiating elements of the array;

t_o =scan start time; and

θ_s is the beam scan rate in radians/sec.

The samples thus taken by the single receiver are stored in memory in proper order to facilitate processing by a Fast Fourier Transform (FFT) algorithm, the result of which is the reconstructed aperture function of the array. Comparison of the coefficients of the reconstructed aperture function with design values for the corresponding coefficients of the aperture function enables individual identification of radiating elements which are defective in amplitude or phase.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a linear phased array antenna, the beam produced thereby as represented by the aperture function g(kd, t_R), the beam as sampled at time T_r by a plurality of detectors and the beam aperture function as reconstructed by processing the samples from the plural detectors with an inverse Fourier transform.

FIG. 2 is a diagram similar to FIG. 1 except that the beam is sampled at non-uniform intervals of time by a single detector located along a fixed radial angle from the center of array, in accordance with the invention.

FIG. 3 is a functional block diagram of the monitor system of the invention.

FIG. 4 is a simplified flow diagram of the mathematical processing of the beam samples, the beam samples having been taken at non-uniform intervals of time in accordance with the invention, to produce a reconstructed beam aperture function.

FIG. 5 is a functional block diagram of the signal processor used to perform Fourier transformation of the beam samples taken by a single detector at non-uniform intervals of time to produce a reconstructed aperture function.

FIGS. 6 and 6A together, is a flow diagram showing in greater detail than FIG. 4 the mathematical processing of the beam samples to produce a reconstructed aperture function.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates the theory of the invention. A phasedarray antenna 10 is represented schematically as comprising N linearly disposed radiating elements 11 evenly spaced at intervals d along acorporate feed 12 which is supplied with microwave energy by atransmitter 13. Each of the elements 11, exceptcenter element 14 if N is an odd number, is connected to feed 12 through avariable phase shifter 15 and acoupler 16 which conducts a proportion a²_n of the transmitter output power to the element.Center element 14 is connected to feed 12 only through a coupler 16' if N is an odd number. Antenna beam steering is accomplished by electronically adjusting each of the phase shifters to apply a specified phase shift θk to the energy passing therethrough to its associated radiating element. The phase shifts vary along the length of the array, beginning at the left end element k=1 and ending at the right end element k=N, according to the relationship: ##EQU2## where: N is the total number of array elements;

k=1, 2 . . . N, is the index number of the individual array elements;

θ₀ is the maximum scan angle of the array beam, measured from the normal to the array; and

t_R is the beam pointing angle, at time (t_R).

The element weights, or coupling coefficient, a_n are defined by the aperture amplitude distribution function which may take the form shown by the dashedline 20.

The antenna aperture function, which combines the apertureamplitude distribution function 20 and the phase function 21 is given by:

g(kd,t)=a(kd)ε.sup.jp(t)kd                         (3)

where

a(kD) is the amplitude at the kth element;

p(t) kd is the phase gradient at the kth element at time (t); where ##EQU3##

The far field antenna pattern 22, represented by the expression G(p, t), is mathematically equivalent to the Fourier transform of the aperture function, equation (3); i.e. ##EQU4## substituting (3) into (4), ##EQU5##

Assuming, for analytical purposes, that the space extending in the far field from +θ₀ to -θ₀ is provided with a plurality of detectors equiangularly spaced at p_i. The sampled scanning beam is ##EQU6## where ##EQU7##

The inverse discrete Fourier transform of the sequence represented by equation (6), where each of the samples p_i is taken at time t_R is ##EQU8##

Equation (7) is equivalent to the original aperture function, equation (3), for a specific scan angle at time t_r as is shown by the following development: ##EQU9## Let ##EQU10##

It can be shown that ##EQU11##

Substituting (9) into (8) ##EQU12##

Since equation (10) is non-zero only when k=m and since t_R is valid for any t, equation (10) may be rewritten as

f(kd,t)=a(kd)ε.sup.jp(t)kd =g(kd,t)                (11)

which is the original aperture function defined in equation (3).

The possibility of reconstructing the antenna aperture function for a particular scan angle θ_r by extracting the inverse DFT from a sequence of samples taken simultaneously from a plurality of detectors at time t_R is demonstrated by the development of equations (3) through (11).

Sampling the scanning beam using a plurality of detectors positioned in the far field, as assumed in the foregoing is impractical. In accordance with the invention, the beam is sampled by the equivalent of a single detector at p_R located in the far field at a fixed angle θ(t_R), as will now be shown.

Referring to FIG. 2, a single detector at p_R is located in the far field at an angle θ_R between the maximum scan angles of -θ₀ =sin^-1 (λ/2d) and +θ₀ =sin^-1 (λ/2d)

the detector at p_R is strobed to sample the beam at times when the main lobe of the beam is pointed at equally spaced intervals of p_i, such that |p_i -p_i-1 |=sin^-1 (λ/Nd). The sample produced by detector p_R at any sample time t_i is ##EQU13## where ##EQU14##

Assuming left to right beam scan at a constant rate of 20,000°/sec.=349.06 rad./sec. the scan angle θ_i at time t_i after start of scan is: ##EQU15##

Detector p_R is strobed to sample the beam at times t_i given by ##EQU16##

The inverse DFT of the sample sequence G(p_R, t_i) taken at such times t_i is given by: ##EQU17##

Inserting equation (12) into equation (15) ##EQU18##

Substituting equation (9) into equation (16) ##EQU19##

Since equation (17) is equivalent to equation (10), h(md, P_R)=f (md, t_R)=g (md, t) as shown by equation (11). In other words, the inverse DFT of a sequence of samples taken at times t_i by a single detector p_R, as described with reference to FIG. 2, is identical to the inverse DFT of a sequence of samples by detectors p_i taken simultaneously at time t_R, as described with reference to FIG. 1.

The implementation of the method of the invention will next be described with reference to FIG. 3.

FIG. 3 is a functional block diagram of the monitoring system of the invention. An N element phasedarray antenna 10, as described with reference to FIG. 1, is confronted by an integralwaveguide monitor antenna 30.Monitor antenna 30, known in the art, comprises a slotted waveguide extending the length of thearray 10 and adjacent thereto. The slots of the waveguide are so positioned and dimensioned that the signal output online 31 is equivalent to the signal which would be produced by a single receiver located in the far field of the array along a fixed radial from the array. In one embodiment of the invention, such radial is at an angle of 11.5° to the normal to the array.

The monitor signal online 31 is applied to asynchronous detector 32 which also receives a low level reference signal online 33 directly derived from the carrier output oftransmitter 13. The reference output fromtransmitter 13 is passed through a 90°phase shifter 34 then applied as one input to detector 32' which receives as a second input the signal online 31 frommonitor antenna 30.

The output ofdetector 32 is the component of the monitor antenna signal which is in phase with the reference signal fromtransmitter 13. The output of detector 32' is component of the monitor signal which is in quadrature, i.e. at 90° phase, to the reference signal fromtransmitter 13. The outputs ofdetectors 32 and 32' are generally referred to hereinafter, respectively, as the I and Q components, or occasionally as the real and imaginary components, respectively, of the signal frommonitor antenna 30.

The output frommixer 32 is passed through a bandpass filter/amplifier 35 and adetector 36 to the input of an analog to digital (A/D)converter 37. The output of mixer 32' is similarly processed through bandpass filter/amplifier 35' and detector 36' to the input of A/D converter 37'. Suitably, filter/amplifiers 35, 35' are designed to pass and amplify signals in the band of 25-75 KHz.Monitor antenna 30,detectors 32, 32',amplifiers 35, 35'detectors 36, 36' andconverters 37, 37' correspond to the single detector at p_R of FIG. 2.

Converters 37, 37' are controlled by a programmable logic array (PLA) 38 to provide discrete digitized samples of the outputs ofdetectors 36, 36' at intervals t_k.PLA 38 receives synchronizing signals from the arraybeam steering unit 39 and enablesconverters 37, 37' at times during the beam scan cycle determined by formula (14), above. The primary function ofbeam steering unit 39, of course, is to generate signals controlling the setting ofphase shifters 15 of the array, and hence the pointing angle of the array beam.

In the microwave landing system the beam scans in a TO-FRO mode. Starting at the maximum negative scan angle -θ₀ (FIG. 1) the beam scans at the constant rate of 349 rad/sec to the maximum positive scan angle +θ₀, completing the TO scan. After pausing a specified time, the scan direction is reversed and the beam scans from +θ₀ to -θ₀, completing the FRO scan. During consecutive TO and FRO scans,PLA 38 enablesconverters 37, 37' at times t_k (t_k being measured from the start of a TO or FRO scan) to provide two sets of N data samples, one each for the I and Q components of the output ofmonitor antenna 30 for each scan. The data samples fromconverter 37, 37' are placed in buffer storage in asignal processor 40, where they are placed in proper order and condition for transfer to the input of an FFT processor included insignal processor 40.

The generalized functions ofsignal processor 40 are shown in FIG. 4. The antenna aperture function g(kd, t) is complex, hence the in phase (I) and quadrature phase (Q) components of the output ofmonitor antenna 30 must be processed separately, but identically, up to the point of recovery of amplitude and phase for the sampled data. Thus, the window function and post processing operations described below detector at p_R of FIG. 2.

Converters 37, 37' are controlled by a programmable logic array (PLA) 38 to provide discrete digitized samples of the outputs ofdetectors 36, 36' at intervals t_k.PLA 38 receives synchronizing signals from the arraybeam steering unit 39 and enablesconverters 37, 37' at times during the beam scan cycle determined by formula (14), above. The primary function ofbeam steering unit 39, of course, is to generate signals controlling the setting ofphase shifters 15 of the array, and hence the pointing angle of the array beam.

In the microwave landing system the beam scans in a TO-FRO mode. Starting at the maximum negative scan angle -θ₀ (FIG. 1) the beam scans at the constant rate of 349 rad/sec to the maximum positive scan angle +θ₀, completing the TO scan. After pausing a specified time, the scan direction is reversed and the beam scans from +θ₀ to -θ₀, completing the FRO scan. During consecutive TO and FRO scans,PLA 38 enablesconverters 37, 37' at times t_k (t_k being measured from the start of a TO and FRO scan) to provide two sets of N data samples, one each for the I and Q components of the output ofmonitor antenna 30 for each scan. The data samples fromconverter 37, 37' are placed in buffer storage in asignal processor 40, where they are placed in proper order and condition for transfer to the input of an FFT processor included insignal processor 40.

The generalized functions ofsignal processor 40 are shown in FIG. 4. The antenna aperture function g(kd, t) is complex, hence the in phase (I) and quadrature phase (Q) components of the output ofmonitor antenna 30 must be processed separately, but identically, up to the point of recovery of amplitude and phase for the sampled data. Thus, the window function and post processing operations described below are performed on one sample set, say the I samples, and the results are stored in RAM in appropriate order, then the same operations are performed on the Q sample set and the results are stored in RAM in proper order, separately from the processed I samples. The FFT algorithm combines the I and Q samples in a prescribed manner, as known to those skilled in the art. Finally the processed I and Q samples are combined to provide the amplitude and phase of the reconstructed aperture function at each of the sample points.

Referring to FIG. 4, the data samples from A/D converters 37, 37' are stored inRAM 50 in two ordered sequences G_k^I (converter 37) and G_k^Q (converter 37') and k=0 . . . N-1.

These sequences are modified by awindow function 51 to reduce the data truncation effects caused by utilizing an antenna scan angle which is less than the theoretical maximum scan angle. For example, the element spacing of a particular antenna may be such as to permit a maximum scan angle of ±60°, but such antenna is actually scanned ±40° and the sample data only covers the actual scan.

A choice of known window functions is available and a suitable such function is the Hanning window comprising a sequence of constants C_H (k) given by: ##EQU20##

These constants are precomputed, stored in a look-up table and are called up as multiplying factors in accordance with the index of the complex sample G_k entering the window function.

After processing by the window function the complex sample sequence is stored as a modified complex sequence U_k where ##EQU21##

The complex U_k data sequence is next passed through an Inverse Fast Fourier Transform (IFFT) 52 to provide the data sequence V_k. As is known to those skilled in art, the IFFT involves a multiplicity of "butterfly computations"; for example see the article "What is the Fast Fourier Transform?" IEEE Transactions on Audio and Electroacoustics, pp. 45 ff. v. AU-15, no. 2, June 1967.

The processing of the data sequence U_k by the IFFT to produce the data sequence V_k is expressed mathematically as: ##EQU22## where ##EQU23##

The transformed complex data sequence V_k must be referenced to the phase center of the antenna for the reconstructed aperture function h(kd, P_R) to correspond to the actual aperture function g (kd, t_R). When N, the total number of radiating elements in an array is an odd number, the phase center is the center element of the array. V_k can then be transformed directly into polar coordinates a_k, φ_k without requiring any post IFFT processing.

When N is an even number, the phase reference is mid-way between the two center-most array elements and the V_R sequence output ofIFFT 52 must be modified by a series of coefficients C_pp so that the reconstructed aperture has the same phase reference as the actual aperture. The C_pp coefficients are given by: ##EQU24##

The operation of equation (23) is carried out inblock 53 for both the real and imaginary parts of V_k to produce the modified sequence: ##EQU25##

The amplitude a_k and phase φ_k for each of the antenna radiating elements are readily computed from: ##EQU26##

Signal processor 40 comprises the elements shown in the block diagram of FIG. 5. The constants C_H (K); W^nk_N ; C_pp (k-1) are precomputed and stored in read-only memories (ROM) 54, 55, 56. The arithmetic operations represented byblocks 51, 52 and 53, FIG. 4, are carried out by a multiplier-accumulator (MAC) 57 under the command of amicrocoded controller 61. The I and Q data samples fromconverters 37, 37' are stored in random access memory (RAM) 50.RAM 62 provides storage for the results U_K, V_K and g_K ofcomputations 51, 52 and 53.Scratch pad RAM 63 provides buffer storage for transferring data betweenRAMs 52, 62 andMAC 57. Abi-directional data bus 64 interconnects RAMs 50, 62, 63,MAC 57 andmicroprocessor 40 for the exchange of data therebetween.Data bus 65 transmits data from a selected one of ROMs 54-56 to the Y input register ofMAC 57.Controller 61, under executive control ofmicroprocessor 41, as indicated bycontrol lines 66 and 66', addresses RAM and ROM locations and controls the transfer gates of thedata buses 64 and 65.Controller 61 contains a microinstruction set for performing the operations represented by blocks 51-53 of FIG. 4. All of the elements of FIG. 5 are available as standard commercial integrated circuits.

The executive program forsignal processor 40 is illustrated in FIG. 6. Samples taken during an antenna scan, say a TO scan, are stored inRAM 50. At the beginning of the following FRO scan the data stored inRAM 50 is transferred toRAM 63.RAM 50 is then clear to receive samples collected during the FRO scan while data from the previous TO scan is being processed insignal processor 40. Thefirst step 80 of the program is to adjust the numerical vallues of the I and Q samples sequence taken during one scan of the antenna (TO or FRO) for gain variations between the Ichannel comprising elements 32, 35-37 and the Q channel comprising elements 32', 35-37, FIG. 3.

If the total number N of data samples is such that log₂ N does not equal an integer, a sufficient number of zero value samples are added at 81, to the sample sequence to cause the logarithm of the increased number of samples to be an integer. Preferably, the zero value samples are added at the beginning and at the end of the data sequence. This is a well-known artifice to facilitate processing of the data by means of an FFT alogrithm. This technique affects all computations of T_k, C_H, W_N^nk and C_pp.

If the data undergoing processing has been collected during a FRO scan,decision block 82 causes the order of data samples to be reversed at 83 prior to multiplication by the constants C_H (K) at 84. Otherwise, the samples are processed at 84 in the order in which they were collected.

Window function 84 is carried out by a subroutine incontroller 61 which transfers the appropriate constant C_H (K) fromROM 54 to theY input 68 ofMAC 57, transfer appropriate sample G_K fromRAM 63 to theX input 69 ofMAC 57, and stores the XY products from product accumulator 71 ofMAC 57 inRAM 62. After the data sequence G_K is processed into the data sequence U_K,controller 61 clearsRAM 63 and then transfers the sequence U_K intoRAM 63 in bit reversed order, following the program given below forLoop #1.

Inverse FFT 85 is performed in two loop operations.Loop #1 directs the transfer fromRAM 62 to RAM 63 of the samples comprising the U_K sequence in "bit reversed" order. Loop #2 performs the "butterfly" FFT operation. Basically, Loop #2 breaks the total FFT into two-point FFT stages, cascading those stages to compute the desired output. A detailed explanation of the "bit reversal" and "butterfly" procedures is given in the book "Introduction to Discrete-Time Signal Processing" by S. A. Tretter, 1976, John Wiley, publisher. The program forLoop #1, written in FORTRAN is generalized form is:

______________________________________DO Loop #1                                                    ______________________________________                                                N=2**M                                                                    N2=N/2                                                                    N1=N-1                                                                    J=1                                                                       DO 3 I=1,N1                                                                 IF (I.GE.J)GOTO 1                                                         T=X(J)                                                                    X(J)=X(I)                                                                 X(I)=T                                                                    K=N2                                                                      IF (K.GE.J)GOTO 3                                                         J=J-k                                                                     GOTO 2                                                                  J=J+k                                                                     END                                                           ______________________________________

AfterLoop #1 is completed, Loop #2 is performed using the bit reversed U_K samples now stored inRAM 62 and the W^nk constants stored inROM 55 as the X and Y inputs toMAC 57 and storing the V_K outputs of product accumulator 71, according to the following program for Loop #2:

______________________________________                                           DO Loop #2                                                         ______________________________________                                           PI=3.141592653589793                                                      DO 5 L-1, M                                                                LE=2**L                                                                   LE1=LE/2                                                                  U-(1.0,0.0)                                                               W-CMPLX(COS(PI/LE1),SIN(PI/LE1))                                          DO 5 J=1,LE1                                                               DO 4 I=J,N,LE                                                              ID-I+LE1                                                                  T-X(ID)*U                                                                 X(ID)-X(I)-T                                                              X(I)=X(I)+T                                                             U=U*W                                                                     RETURN                                                                    END                                                               ______________________________________

After transformation of the U_K sequence into the V_K sequence, the V_K sequence is post-processed, as shown byblock 53, FIG. 4 to establish the phase reference for the antenna array at the mid-point of the V_K sequence. The result is the sequence g_k. Post-processing of the sequence V_K is carried out by the sub-routine 86, shown in greater detail in FIG. 6A.

If the antenna array is contructed with an odd number of radiating elements, the phase reference is the center element of the array. Post-processing of the V_K samples is then unnecessary, as g_k =V_K. Obviously, in such a case, block 53 can be eliminated from FIG. 4 andROM 56 can be eliminated from FIG. 5.

If the antenna array is constructed with an even number of radiating elements, the phase reference will lie at a point on the array which is midway between the two centermost elements of the array. In the latter case, post-processing of the V_k samples bysubroutine 86 to transform the V_K sequence into the g_k sequence is required so that the amplitude a_K and phase_K at each of the antenna elements can be properly calculated from the g_k data.

Referring to FIG. 6A, thefirst step 87 ofsub-routine 86 is to remove any 180 degree phase gradients which may be present in the samples of the V_K sequence, i.e., only the absolute values of the V_K samples are processed. Steps 90-94 functionally illustrate the instructions given bycontroller 61 toMAC 57 in summing C_pp (k-1)V_K over 1=0,N-1. As each g_k sample is input fromROM 62 to register 69 ofMAC 57, block 93 calls the appropriate C_pp (k-1) constant fromROM 56 for input to register 68 and the product is added to the sum contained in accumulator 71 until all 1=0,N-1, values of C_pp (k-1) for the kth sample have been processed. Then the next in order k sample of V_K is similarly processed. After all N samples of the sequence V_K have been so processed, transformation of the V_K sequence into the g_k sequence has been accomplished and the program of FIG. 6 is continued.

Referring to FIG. 6,instruction 100 directs the transfer to RAM 63 of the gk samples stored inRAM 62 at the end of the sub-routine of FIG. 6A. There the gk samples are rearranged in numerical order and normalized. Theninstruction 101 directs the computation of amplitude a_K and phase φ_K for each antenna radiating element, applying formulas (25) and (26). Upon computation of a_K and φ_K for the TO antenna scan,decision block 102 returns to block 80 to perform the program of FIG. 6 for the g_k samples taken during the FRO scan. When a_K and φ_K have been computed,instruction 103 averages a_k and φ_k computed from the TO and FRO scan data and exits the program.

The averaged a_k and φ_k data are compared bymicroprocessor 41 with corresponding stored design or calibration a_k and φ_k values for each antenna radiating element. Any antenna element showing more than a tolerable difference is identified in a print-out fromprinter 42 for for remedial action.

The system of the invention not only provides on-line monitoring of an operational MLS, but it is also useful for initial calibration of the MLS antenna array. In that case a_k and φ_k values computed from scan data are compared with corresponding design values. Any radiating element showing an intolerable variance between the design and computed values is identified for either physical or electronic treatment. That is, it may be necessary either to rework or to replace certain of thephase shifters 15 orcouplers 16 to correct anomalies in a_k or it may be possible to correct anomalies in φ_k by adding a fixed compensating factor to the φ_K steering command frombeam steering unit 34 for the faulty element. If such compensating factors are added to φ_K, the values of φ_k as adjusted, i.e., the calibration values, as used as comparison standards during monitoring operation, rather than design values. ##EQU27##

Claims (19)

The invention claimed is:

1. The method of monitoring the performance of a scanning phased array antenna to identify faults in said antenna, said antenna having a plurality of radiating elements and plurality of phase shifters associated with said elements to control the direction of a beam of energy transmitted by said radiating elements, said antenna scanning between the maximum angles of +θ_o and -θ_o, θ being the angle between the axis of said beam and the normal to the axis of the array of said antenna, comprising: collecting, from a single detector of signals transmitted by said antenna, at equal increments of arcsin θ, a plurality of signal samples;

analyzing said collected samples by means of a Fourier transform to provide a sequence of data indicating the amplitude and phase of the signal radiated by each of said antenna radiating elements when the beam of said antenna was directed toward said detector; and

comparing the data of said sequence with known values of the amplitude and phase of the signal radiated by each of the radiating elements of said antenna when said antenna is perfectly functioning and the beam thereof is directed toward said detector.

2. A method as claimed in claim 1, wherein:

said antenna radiates energy having a wavelength λ;

said plurality of radiating elements of said antenna comprises a total number N, each of said elements being separated by equal distances d;

said beam is a scanning beam which scans at a constant rate equal to θ_s ; and

said collected samples comprise a sequence of samples taken at times t_k, where t_k is given by: ##EQU28## where k=0,1, . . . N-1, and

t_o =time at the start of scan.

3. A method as claimed in claim 1, wherein each of said collected samples is a complex number comprising an in-phase component I and a quadrature component Q and, wherein said step of analyzing said collected samples includes the step of:

multiplying each of said I and Q components by a window function constant prior to said step of analyzing said collected samples by means of a Fourier transform; and

said window function constant having the property of modifying said collected samples to compensate for the loss of data due to said step of collecting signal samples between the maximum scan angles of -θ_o and +θ_o when θ_o is less than arcsine λ/2d, λ being the wavelength of the energy radiated by said antenna and d being the distance separating each of said radiating elements of antenna.

4. A method as claimed in claim 3, wherein said window function constant is a series of constant numbers C_H (k) and each number of said series is given by the formula: ##EQU29## where k is the order in which respective ones of said samples are collected, and k=0, 1, . . . N-1, N being the total number of said radiating elements of said antenna.

5. A method as claimed in claim 3, wherein said step of analyzing said collected samples further includes the step of:

adding, after said step of multiplying said collected samples by said window function constants and prior to analyzing said samples by means of a Fourier transform, a further number of zero-value samples to said collected samples to provide a data sequence U_M until the total number of said collected samples and said added zero-value samples in said sequence U_K is equal to a quantity comprising an integer power of the number 2.

6. A method as claimed in claim 5, wherein said step of analyzing said collected samples by means including a Fourier transform produces a second data sequency V_K and, wherein said step of analyzing comprises the process expressed mathematically as: ##EQU30## where ##EQU31##

7. A method as claimed in claim 6, wherein the total number of radiating elements of said antenna is an even number, with said radiating elements being linearly disposed and equally spaced apart along the length of said antenna and, wherein the phases of the signals radiated by said radiating elements vary linearly along the length of said antenna, wherein said step of analyzing said collected samples includes the steps of:

multiplying each of the samples of said second data sequence V_k by individual post-processing constants C_pp to produce a third data sequence g_k ;

calculating from said third data sequence g_k the amplitude and phase of the signal radiated by each of said radiating elements; and

said constants C_pp having the property of modifying said samples of said data sequence V_k so that said phases calculated from said data sequence g_k are with reference to the phase at a point midway along the length of said antenna.

8. A method as claimed in claim 7, wherein said individual constants C_pp are given by the formula: ##EQU32## k being the order of each of said samples in said data sequence V_k and k-0, 1, . . . N-1; 1 being the series 1=1, 2, . . . N.

9. A method as claimed in claim 6, wherein the total number of radiating elements of said antenna is an odd number, with said radiating elements being linearly disposed and equally spaced along the length of said antenna, each said radiating element being identified by a number k according to the order of location of said element along the length of sad antenna;

said second data sequence V_k being complex with each sample k thereof being related to a corresponding k one of said radiating elements;

said sequence V_k having a real component R and an imaginary component I;

and wherein said step of analyzing said collected samples to provide the amplitude and phase of the signal radiated by each of said radiating elements includes the step of calculating the amplitude a_k of the signal radiated by each said radiating element k from the formula: ##EQU33## and the step of calculating the phase φ_k of the signal radiated by each said radiating element k from the formula: ##EQU34##

10. The method of calibrating a scanning phased array antenna to adjust the performance thereof to conform to design spcifications therefor, said antenna having a plurality of radiating elements and a plurality of phase shifters associated with said elements to control the direction of a beam of energy transmitted by said radiating elements, said beam being a scanning beam which scans between the maximum angles of -θ_o and +θ_o, θ being the angle between the axis of said beam and the normal to the axis of the array of said antenna, comprising:

collecting, at equal increments of arcsin θ, from a single detector of signals transmitted by said antenna, a plurality of signal samples;

analyzing said collected samples, by means including a Fourier transform, to provide a sequence of data indicating the amplitude and phase of the signal radiated by each of said antenna radiating elements when said beam of said antenna was directed toward said detector;

comparing the amplitude of the signal radiated by each of said radiating elements as given by said sequence of data with design values of amplitude for the signal intended to be radiated by each of the radiating elements when the beam thereof is directed toward said detector; and

adjusting the amplitude of the signal radiated by any one of said radiating elements of said antenna to conform to the design value of the amplitude of the signal intended to be radiated by that said one radiating element when the amplitude of the signal radiated by that said one radiating element as given by said sequence of data differs from said design value therefor.

11. The method of calibrating a phased array antenna as claimed in claim 10 with the additional step of:

comparing the phase of the signal radiated by each of said radiating elements as given by said sequence of data with design values of the phase for the signal intended to be radiated by each of the radiating elements when the beam thereof is directed toward said detector; and

adjusting the phase of the signal radiated by any one of said radiating elements of said antenna to conform to the design value of the phase of the signal intended to be radiated by that said one radiating element when the phase of that said one radiating element as given by said sequence of data differs from said design value therefor.

12. A method of calibrating a phased array antenna as claimed in claim 11 wherein:

said antenna radiates energy having a wavelength λ;

said plurality of radiating elements of said antenna comprises a total number N, each of said elements being separated by equal distances d;

said beam is a scanning beam which scans at a constant rate equal to θ_s ; and

said collected samples comprise a sequence of samples taken at times t_k, where t_k is given by: ##EQU35## where k=0, 1, . . . N-1, and

t_o =time at the start of scan.

13. The method of calibrating a phased array antenna as claimed in claim 12, wherein said antenna includes a beam steering unit and said phase shifters are adjustable under the control of command signals issued by said beam steering unit to each of said phase shifters and wherein the step of adjusting the phase of the signal radiated by any one of said radiating elements to conform to the design value of the phase intended to be radiated by that one radiating element includes:

modifying the command signal issued by said beam steering unit to that said one radiating element to include a compensating factor, said compensating factor being such as to alter the phase of the signal radiated by that said one of the radiating elements to conform to said design value therefor.

14. A system for monitoring the performance of a phased array antenna to identify faults in said antenna, said antenna having a plurality of radiating elements and a plurality of phase shifters associated with said elements, a transmitter and feed means for distributing output from said transmitter to said phase shifters and said radiating elements, said phase shifters and said radiating elements cooperating to shape the output received by each from said transmitter into a beam of energy and to control the direction in which said beam is pointed, comprising:

means for receiving the signal radiated by said antenna to provide a received signal;

means for synchronously detecting said received signal to provide a first component thereof which is in phase with said output of said transmitter and a second component thereof which is in quadrature phase with said output of said transmitter;

means for amplitude detecting said first component to provide a first analog signal which is proportional to the amplitude of said first component;

means for amplitude detecting said second component to provide a second analog signal which is proportional to the amplitude of said second component;

a first analog to digital (A/D) converter for converting said first analog signal to a first digital signal;

a second analog to digital (A/D) converter for converting said second analog signal to a second digital signal;

means for controlling said first and second A/D converters whereby said first and second A/D converters provide discrete digital samples of said first and second analog signals with said digital samples being separated from one another by non-uniform intervals of time, said first and second digital samples forming a sequence of data which is in the form of a complex number; and

means for mathematically processing said sequence of data to provide the value of the amplitude and phase of the signal radiated by each of said radiating elements of said antenna when said beam of said antenna is pointed in the direction of said means for receiving.

15. A system as claimed in claim 14, wherein said means for mathematically processing includes:

means for performing a Fourier transform on said sequence of data to provide a second sequence of data from which said amplitude and phase of said signal radiated by each of said radiating elements is computed.

16. A system as claimed in claim 15, wherein the beam transmitted by said antenna is a scanning beam and said beam scans between the maximum angles -θ_o and +θ_o, θ being the angle between the axis of said beam and the normal to the axis of the array of said antenna, and wherein said means for controlling said first and second A/D converters enables said converters to provide said samples at successive equal increments of arcsine φ.

17. A system as claimed in claim 16, wherein said radiating elements are disposed in a linear array with said radiating elements being spaced apart by equal distances d and wherein said means for controlling said first and second A/D converters enables said converters to provide said samples at times t_k given by: ##EQU36## where λ is the wavelength of the energy radiated by said antenna;

d is the distance between each of said radiating elements;

N is the total number of said radiating elements;

t_o is the time at the start of scan; and

k=0, 1, . . . N=1.

18. A system as claimed in claim 17, wherein said means for receiving the signal radiated by said antenna includes a monitor antenna comprising:

a slotted waveguide, said waveguide extending the length of said linear array and being positioned adjacent thereto.

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